Using different server SQL mode settings on the master and the
slave may cause the same
statements to be handled differently on the master and the
slave, leading the master and slave to diverge. For best
results, you should always use the same server SQL mode on the
master and on the slave. This advice applies whether you are
using statement-based or row-based replication.
If you are replicating partitioned tables, using different SQL modes on the master and the slave is likely to cause issues. At a minimum, this is likely to cause the distribution of data among partitions to be different in the master's and slave's copies of a given table. It may also cause inserts into partitioned tables that succeed on the master to fail on the slave.
For more information, see Section 5.1.10, “Server SQL Modes”. In particular, see SQL Mode Changes in MySQL 5.7, which describes changes in MySQL 5.7, so that you can assess whether your applications will be affected.